Third seed Pegula beat qualifier Katherine Sebov (24) 6-3 6-1 and will next face fellow American Danielle Collins (29) while sixth seed Gauff eased past Rebecca Marino 6-4 6-3 to set up a battle with Russia's Anastasia Potapova (21).
Pegula, a semi-finalist last year in Miami who lives about 40 minutes away from the tournament venue, converted five of her nine break point opportunities and found her groove as her first career match against Sebov wore on.
"I just went out the and took care of business ... fought through some tricky moments in the first set but then I think I started to free up after that," Pegula said in her on-court interview.
Pegula opened the match with a break but Sebov broke back at love to level at 2-2 before the American took control with another break for a 3-2 lead and closed out the first set in 35 minutes.
Pegula had a much easier time in the second set where she broke early for a 2-0 lead and dropped just two points on serve the rest of the way.
Gauff, who resides in Southeast Florida and is coming off a run to the quarter-finals in Indian Wells, also converted five of her nine break point chances and twice came back from a break down in the second set.
"Playing at home is something I look forward to but it's also a little extra pressure because you know everybody wants you to do well here." said Gauff.
With the victory, Gauff broke a stalemate with Anastasia Pavlyuchenkova and now holds the record for most wins (34) at WTA 1000 events before turning 20.
In other second-round action, Belgian Elise Mertens (27) beat Russian eighth seed Daria Kasatkina (25), Spanish 21st seed Paula Badosa (25) overcame Germany's Laura Siegemund (35) and China's Zheng Qinwen (20), the 23rd seed, beat Romanian Irina-Camelia Begu (32).
RYBAKINA EYES 'SUNSHINE DOUBLE'
Later on Thursday, Wimbledon champion Rybakina, fresh off her triumph at Indian Wells, closed out the evening session with a hard-fought 7-5 4-6 6-3 win over Russia's Kalinskaya.
Kalinskaya tested the world number seven throughout the contest and broke early on, but with the Russian leading at 5-3, Rybakina was able to raise her level and win four straight games to take the first set.
Rybakina's resurgence briefly took the wind out of Kalinskaya's sails, and the Russian gifted her opponent a 3-1 lead in the second set with a couple of errant shots.
With her back against the wall, Kalinskaya mounted a spirited comeback to pull ahead at 5-4 before holding serve to level the match.
The pair traded breaks early in the decider, but Rybakina got over the finish line after more than two hours on court, breaking to take a 5-3 lead and then completing the job when Kalinskaya sent a backhand into the stands.
"It's not easy, I had just two days to adapt (after Indian Wells)," Rybakina said in her on-court interview.
"It was a tough match. I'm really happy I could win in the end. I had the opportunity to close in two sets but I made some silly mistakes and she really returned well."
If Rybakina lifts the title in Miami, she would become only the fifth woman to win the Indian Wells and Miami tournaments back-to-back, a feat known as the "Sunshine Double" given the tournaments' locations in California and Florida.
Rybakina next faces Spain's Badosa.
On the men's side, Chilean qualifier Cristian Garin (26), who made a surprising run to the fourth round at Indian Wells, beat Marcos Giron (29) 6-2 2-6 6-4 to reach the second round in Miami.
Austrian wildcard Dominic Thiem (29) will kick off the evening session with a first-round clash against Italy's Lorenzo Sonego (27) while Frenchman Richard Gasquet (36) battles Australian lucky loser Christopher O'Connell (28).
